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Egg-Citing Eggs-Perience

A woman went to a local outdoor market with 20 eggs, another woman went with 30 eggs, and a third woman went with 50 eggs. All three women sold their eggs at the same rate and received the same amount of money. How could this be?

Note: M.N. (Bellingham) has already submitted the clever solution of "0 eggs/hr. (if the rate is time) or $0/egg (rate is cost per egg)." So, let's remove that possibility and assume that the rate exceeded the infamous value of 0.


Source: H.V. (Bellingham)

Hint: When thinking in terms of a rate, think in terms of both "dozen eggs" and "single eggs."


Solution Commentary: First, a note from the teacher (H.V.) who submitted this problem: Different students will attack this problem in different ways. Although a formula may exist for solving this problem, I would be willing to bet most students trying this problem wouldn't know the formula. Some may look for a formula, others may just use trial and error, while others may be more systematic...They may attempt to solve this problem by dividing the different groups into an equal number of sets, which would put them on the right track since the dozen eggs and single eggs are the key. Some may also interpret the "same rate" as determined by the number of eggs they start out with, instead of charging the same prices, and go at it from that angle.

The eggs were sold at the following rate: Ten cents for each even dozen and five cents for each single egg beyond the even dozen. Thus, each woman received fifty cents for her eggs.

Also, M.N. (Bellingham, WA) adds this note, in addition to his removal of the "zero" case: This solution doesn't fit with the clue, but the eggs could be sold by weight (5 XL chicken eggs weigh the same as 8 Small chicken eggs). Here's a nice picture:

Eggs Eggs Eggs

I bet with a little research, we could find birds where 'weight 20 eggs from type A' = 'weight 30 eggs type B' = 'weight 50 eggs type C', but I've got too much to do today to track that down!